Mathematics Curriculum for Quiz – Level 5
1. Relations and Functions
- Types of functions (One-to-one, Onto, Bijective)
- Inverse Trigonometric Functions (Principal values, domains, ranges)
- Composite Functions and Inverses
2. Algebra
- Matrices: Operations, Determinants, Inverse, Rank, Trace, and Eigenvalues
- Determinants: Calculation and properties
3. Calculus
- Differentiation: Derivatives of various functions (algebraic, trigonometric, exponential) and higher-order derivatives
- Integration: Indefinite and definite integrals, and integration techniques (substitution, by parts)
- Applications: Finding area under curves and volume or surface area of 3D objects
- Differential Equations: Order, degree, and general solutions
4. Vectors and Three-Dimensional Geometry
- Vectors: Dot product, cross product, projections, and angles
- 3D Geometry: Equations of lines and planes
- Surfaces: Equations of spheres, cones, cylinders, ellipsoids, and hyperboloids
5. Linear Programming
- Objective functions and constraints
- Feasible regions and optimal solutions (corner point method)
- Slack variables and simplex method
6. Probability
- Independent and mutually exclusive events
- Conditional probability
- Addition and multiplication rules